Question: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-8x-8y &= 1 \\ -x+6y &= -6\end{align*}$
Begin by moving the $y$ -term in the second equation to the right side of the equation. $-x = -6y-6$ Divide both sides by $-1$ to isolate $x$ $x = {6y + 6}$ Substitute this expression for $x$ in the first equation. $-8({6y + 6}) - 8y = 1$ $-48y - 48 - 8y = 1$ Simplify by combining terms, then solve for $y$ $-56y - 48 = 1$ $-56y = 49$ $y = -\dfrac{7}{8}$ Substitute $-\dfrac{7}{8}$ for $y$ in the top equation. $-8x-8( -\dfrac{7}{8}) = 1$ $-8x+7 = 1$ $-8x = -6$ $x = \dfrac{3}{4}$ The solution is $\enspace x = \dfrac{3}{4}, \enspace y = -\dfrac{7}{8}$.